The game's first half-chance fell to Glenn Murray, who looped a header over the bar after meeting a good ball into the box.
It was a quiet start to the contest, and Charlton would have been happy with the way they quietened the home fans.
Jordan Obita tried to find a way past the Addicks' resolute defence but his low drive was blocked in an exchange that typified the early stages of the match.
Vetokele eventually got the goal that the visitors deserved when he headed home from Chris Solly's delivery.
Reading should have equalised just before the break, with Simon Cox's initial shot deflecting wide just before Murray's header flew past the wrong side of the post from a corner.